It is often desirable to sample and concentrate particles suspended in a gas for further analysis or detection. Unlike a liquid or a low speed gas flow where the fluid density is relatively constant, the flow of particles suspended in a gas can be rendered highly compressible by inertial effects (Robinson, 1956, Michael, 1968)[1]. As a result, the number of particles per unit volume n at a particular location in the flow may be substantially higher than its initial value no at a reference point upstream. The concentration factor defined asC=n/no  (1)may therefore be much larger than unity, a situation of great practical interest to increase the sensitivity of instruments used for particle detection or analysis. Indeed, since the volumetric sampling flow rate q of such instrument is generally fixed, their sensitivity is increased by a factor C if the particles are concentrated by that factor before being sampled. The usefulness of such a concentrating operation is evident in many situations. For instance, to detect minute quantities of suspended explosive particles at a security control (see U.S. patent application Ser. No. 12/012,771), to monitor the level of cleanness in a room where devices sensitive to particle contamination are being processed, etc.
Under practical situations involving detection or analysis of ambient particles, many particle instruments sample flows typically of 1 lit/min, sometimes considerably more. If one's goal is to concentrate ambient particles by a factor of 1000 prior to detecting them in such instruments, the concentrating device needs to handle very high flow rates of thousands of liters/min. The concentrating device to achieve this goal must therefore be capable of working at very high Reynolds numbers, Re, which for a jet of velocity U formed by a nozzle of diameter D is defined in terms of the fluid's kinematic viscosity v as:Re=DU/v.  (2)
Virtual impactors are common instruments (Chen et al. 1986)[2] that can be used as particle concentrators (Romay et al., 2002)[3]. They involve a jet of gas carrying particles, forced to impact against a virtual wall. The virtual wall is not a solid wall, but an imaginary interface separating the jet from another fluid stream. This second fluid stream is most commonly a confined region of slow moving gas, often a cavity, but it could also be a second relatively strong jet (Willeke and Pavlik, 1978, 1979)[4, 5]. This virtual wall ideally deflects the majority of the impinging gas jet, but is penetrated by some of the suspended particles. In principle, none of the jet gas but some of the particles could be admitted into the cavity region, in which case C would be infinite. In practice, the virtual wall is most often fluid-dynamically unstable and it is conventionally stabilized in virtual impactors by accepting steadily a finite flow rate q of gas into the cavity of slow moving gas. The required minor to major flow ratio q/Q is typically larger than 3%, so that the maximum value of C achievable for particles transferred with high efficiency is generally less than 30. Note that this circumstance not only limits the concentrating ability of virtual impactors. It also reduces considerably their resolving power with respect to that of conventional wall impactors. The reason is that impactors normally capture large particles and not small particles, yet, virtual impactors capture also at least a fraction q/Q of the small particles, and therefore they depart from the ideal high-pass filter impactors they are supposed to be.
An alternative to a single virtual impactor would be a set of m virtual impactors in series, where the limiting concentration factor C1 of a single virtual impactor is raised to the power N of the number of stages: CN=C1N. This approach has been demonstrated by Romay et al. (2002) [3] for the case of two sequential stages of virtual impaction. One problem with the multistage concentrator is that the largest particle size it can pass is limited by particle impaction in the lines connecting one stage to the next.
One of the most effective schemes known to concentrate aerosol particles is so called aerodynamic focusing (Fernández de la Mora and Riesco-Chueca, 1988) [6]. The present invention is therefore concerned with aerosol concentrators hybrid between focusing devices and virtual impactors. The term aerodynamic focusing will be used here to refer to situations leading to relatively large C values. The pioneering ideas leading to the notion of aerodynamic particle focusing are due to Israel and Friedlander (1967) [7], with extensions by Dahneke and Friedlander (1970) [8], Cheng & Dahneke (1979)[9]; Dahneke (1978) [10], Dahneke & Cheng (1979) [11], Dahneke, Hoover, & Cheng (1982) [12], Sinha et al. (1982) [13], and Sinha and Friedlander (1986) [14]. This early work is further described in U.S. Pat. No. 4,383,171, with extensions up to 2006 summarized in Fernández de la Mora (1996) [15], Piseri et al. (2004)[16], and Fernández de la Mora (2006) [17]. In the pioneering work by the groups of Friedlander and Dahneke, and in the most recent developments from McMurry and colleagues, the primary concern was to separate aerosol particles from the gas carrying them, in order to introduce the particles into a vacuum system for further analysis, most often by mass spectrometry. Several characteristics of the earlier manifestations of focusing were that (i) they involved the expansion of a gas into a vacuum; (ii) most of the separation between the gas and the particles occurred in a supersonic jet; (iii) the nozzles used to initiate this supersonic expansion were slowly converging; (iv) the sampling of the particle beam took place many nozzle diameters downstream from the supersonic nozzle; (v) the width of the particle beam obtained was not substantially smaller than the diameter of the sonic nozzle. Consequently, the term focusing could not be used in the absolute sense defined here (C>>1), but only in a relative sense comparing particle concentrations to gas concentrations. In other words, the particles kept approximately their initial concentration (or decreased it moderately), while the concentration of gas molecules diminished greatly. The term focusing could however be used in the different sense that, as shown by Friedlander and colleagues, the particles in the beam did cross from one side of the symmetry axis to the other.
The first demonstration of focusing in the specific sense of interest to this invention (C >>1) was given by Fernández de la Mora and Riesco-Chueca (1988) [6]. (i) They showed that focusing can occur also in subsonic and low speed flows, and may arise as a true singularity, with C tending to infinity. This singular effect, however, is limited by so-called geometric aberration, due to the fact that the point at which particles of a given size cross the axis of symmetry varies slightly as a function of their initial distance to the axis of symmetry. (ii) They demonstrated practical situations with C>1000. (iii) They showed that the slowly converging nozzles used previously had poor performance, while nozzles with more rapidly converging walls (including wedges with half angles α>π/2) could focus substantially smaller particles. (iv) They introduced the concept of the critical focusing Stokes number Scrit, above which particles initially near the axis would cross the axis, noting that subcritical particles do not cross the axis, critical particles cross it at infinity, and supercritical particles cross it at finite distances from the nozzle. FIG. 1 shows schematically in a standard scientific convention the evolution of said finite distance as a function of the Stokes number. The logarithm of the Stokes (Log(S)) is represented in the axis of abscissas while the distance at which particles cross the axis of the nozzle (f) is represented in the axis of ordinates.
The Stokes number S is here defined conventionally as (Friedlander, 1977) [18]S=τU/D,  (3)based on jet speed U, nozzle diameter D and the stopping time τ of a particle. τ is defined as the time required to reduce the speed of the particle by a factor of e (Euler's number) when flying though gas at rest. In this context it is also useful to define the aerodynamic size of a particle as the diameter of a spherical particle whose resistance to motion in the gas is linear with its velocity relative to the gas, and whose density and stopping time τ are the same as those for the real particle
The contributions of Fernández de la Mora and Riesco-Chueca (1988) [6] were primarily theoretical, with additional numerical examples restricted to two-dimensional flows. However, the general validity of their picture has been confirmed by experiments with axisymmetric nozzles (Rao et al, 1993 [19], Fuerstenau et al., 1994[20]). Easily fabricated thin-plate orifice nozzles (α=π/2) have subsequently been most often used for aerodynamic focusing. However, Mihda and Wexler (2003) [21] have confirmed the advantage of even larger convergence cone angles, while both these authors and Piseri et al (2004) [16] have contributed improved geometries capable of focusing particles with unusually small Stokes numbers.
While useful to concentrate sharply particles within a narrow range of sizes (Stokes numbers S), the work of Fernández de la Mora and Riesco-Chueca (1988) did not solve the problem of concentrating simultaneously a wide range of particle sizes, which is the concern of the present invention. An important step in that direction came from two independent lines of work, based on many (rather than just one) acceleration and deceleration steps. This scheme will be referred to as multiple shot focusing. As shown by Robinson (1956) [1], one suitably designed stage of acceleration and deceleration leads to a net concentration, C1>1. For small S, C1 differs only slightly from unity. But a sequence of N such steps in series produces a concentration factor C=C1N, leading at sufficiently large N to a highly concentrated or “focused” aerosol, even at modest S values. This behavior was first seen in some striking calculations by Maxey (1987) [22] involving spatially periodic flows, which have inspired a large number of subsequent fluid dynamical investigations (i.e., Gañán-Calvo & Lasheras, 1991[23]; Tio, Liñán, Lasheras, & Gañán-Calvo, 1993[24, 25]; Martin & Meiburg, 1994[26]; Rubin, Jones, & Maxey, 1995[27], among many others). This rich line of theoretical work has had no observable effect on practical aerosol concentrators. Multiple shot focusing was first brought to practice in general as well as introduced conceptually in the aerosol literature by McMurry and his colleagues (Liu et al. 1993, 1995a, 1995b [28, 29]), without connection to Maxey's precedent. These authors used primarily sharp edge orifice nozzles, and introduced the widely accepted terminology aerodynamic lens to refer to each individual nozzle followed by a deceleration region. Their work has had considerable impact on the important problem originally addressed by Friedlander and Dahneke: determining the chemical composition of suspended particles after introducing them into a vacuum.
Some of these ideas have been protected in U.S. Pat. No. 5,270,542. This patent is restricted to situations where there is a relatively rapid lateral expansion of a gas accompanied by a relatively slow lateral expansion of the aerosol particles. Since it is not possible to achieve such a rapid expansion of a gas under subsonic or even moderately supersonic conditions (except under very small Reynolds numbers that would severely restrict the usefulness of the invention), the U.S. Pat. No. 5,270,542 patent addresses exclusively situations initiated by the formation of a highly supersonic jet. Other related patents exist, similarly restricted to form particle beams for introduction into a vacuum, such as U.S. Pat. No. 6,040,574. Highly supersonic jets are indeed unavoidable when introducing an aerosol initially at atmospheric pressure into a vacuum. But they are undesirable in applications such as those pursued here, where the process of particle concentration tends to take place close to the original pressure of the gas-particle suspension (often atmospheric pressure). Even under conditions where a moderately supersonic jet is advantageous, the present invention considers only initial expansion ratios po/p1 for the jet pressure of at most 10.
From the point of view of the present invention, the main advantage of multiple shot focusing with approximately periodic nozzles is the considerably wider range of S values that can be focused (typically from S below 0.1 up to above 1), and the higher concentration factor C generally achievable, compared to what is possible with single shot focusing. The multiple shot approach is in principle not restricted to the formation of aerosol beams for introduction into a vacuum. However, in practice, it is not readily extended to applications involving atmospheric pressures and high gas flow rates. The reason is that the flow configurations so far employed or proposed lead to transition to turbulence and make the focusing devices inoperative at relatively low Reynolds numbers. For instance, according to Eichler et al. (1998; FIG. 5[30]), the focusing performance of the nozzle geometry most commonly used in aerodynamic lenses (a sharp edge orifice) degrades rapidly at Re above 70. The 5,270,542 patent describes four different types of focusing lenses, all of which lead to detachment and reattachment of the streamlines (Liu et al. 1995a, b). As is well known to those skilled in the art, these configurations can be stable only at relatively low Re. This restriction is generally compatible with particle beam forming applications, but can be readily seen to be inadequate for most atmospheric pressure applications. For instance, for air at ambient conditions, with a nozzle diameter D=1 mm, the flow rate at Re=70 is Q=0.33 lit/min.
Some remarks are pertinent here on solutions previously proposed to match a receiving tube or collector and an incoming jet in an aerosol concentrator. Both virtual impactors and the various skimmer designs used for introducing focused aerosol beams into a final vacuum stage have the same configuration of a jet impinging on a plate or a cone with an aligned orifice. This is a special case of a flow past a cavity with a free shear layer at the virtual wall, which is subject to a Kelvin-Helmholtz type instability with feedback due to the mobile stagnation point at the border of the cavity. As a result, there is a net oscillatory penetration of gas jet into the cavity. The aerodynamic configuration in the collector cavity needs to be sufficiently stable to enable safe passage of the smallest particles in the range of interest into the steady region of the cavity. In the case of virtual impactors, the instability is solved via a relatively high suction through the collector orifice, which limits the concentration factor C. In beam forming devices, the instability is resolved by two circumstances: First, the Reynolds number is already relatively low through the focusing region. Second, it becomes even smaller in the low pressure region at which the beam is admitted to the high vacuum region of the device. But this solution is inevitably associated to low flow rates.
The advantages in this respect of a focusing virtual impactor have been noted by Fuerstenau et al. (1994) [20]. If the accelerating nozzle concentrates the particles into a region of diameter df substantially smaller than the nozzle throat diameter D, the collector orifice diameter dc can be made comparable to df. This reduces the flow Reynolds number in the region of the sampling orifice by a potentially large factor (dc/D)2. The reason is that the characteristic length is reduced by the factor dc/D, while the flow velocity in this region (stagnation point flow region when there is little or no suction) is also reduced by another dc/D factor. Unfortunately the potential advantage noted by Fuerstenau et al. (1994) [20] is restricted to single shot focusing, which can by its very nature concentrate only a relatively modest range of particle sizes. It could via multiple shot focusing be turned into a particle concentrator of wide size range, but only at flow rates too small to meet our present objectives.
In conclusion, there are presently no known solutions to the related problems of achieving                (i) virtual impactors with sampling flow ratios q/Q smaller than 1%        (ii) single-stage virtual impactor concentrators with C>100        (iii) multiple shot focusing concentrators achieving C>100 at Re>100        (iv) focusing devices with a wide particle size range operating at Re>100Furthermore, the only aerodynamic concentration scheme known to achieve C>100 at high Re (Romay et al. 2002) [3] uses at least two conventional virtual impactors in series. But this system is limited in the largest particle size it can handle by particle losses on the flow lines leading from the first to the second virtual impactor stage.        